A mathematical model of the progression of cells through the mitotic cycle under continuous low-dose-rate irradiation is described. The model considers explicitly two special cases: (a) when a fraction of cells disintegrate and disappear after mitosis and (b) when a fraction of cells which have reached mitosis do not progress further but do not disintegrate either. We have established a relationship between the parameters of the model and dose and/or the age of the cell at exposure. This formalism is applied to studies of the effects of dose rate on HeLa cells (Mitchell, Bedford, and Bailey, Radiat. Res. 79, 520-536, 1979; 80, 186-197, 1979). Detailed information on the fraction of cells of a certain biological age at a given chronological time is needed because of the variation in the radioresponse of the cells as a function of age.